Problem: It is possible to choose x>32 in such a way that the value of log10(x2+3) −2log10x is:
Answer Choices:
A. negative
B. zero
C. one
D. smaller than any positive number that might be specified
E. greater than any positive number that might be specified
Solution:
log10(x2+3)−2log10x=log10x2x2+3=log10(1+x23). For a sufficiently large value of x,x23 may be made less than a specified positive number N and so log10(1+x23) may be made less than the specified positive number log10(1+N). Challenge: If, in the problem, the condition x>21 were given instead of x>32, show that then (B) would also be an acceptable answer.